Describe the 3-space graph of the equation z? = y? + x². O A. a circle having radius z in the xy-plane O B. a surface of revolution obtained by rotating the parabola z = y² in the yz-plane about the z-axis O C.a circular cylinder with axis along the z-axis radius z O D. a surface of revolution obtained by rotating the parabola z = x² in the xz-plane about the z-axis O E. a circular cone with vertex at the origin, axis along the z-axis, and semi-vertical angle

Q: Find the equation of a circle in standard form. center at (-4,3) and tangent to the x-axis O…

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Q: Calculate the focus and the directrix of the parabola x^2 + 2 x y + y^2 - 4 x + 2 y - 6 = 0.

A: The given equation of conic is:To find:The focus and directrix of the given parabola.Concept:The…

Q: (b) Find an equation for the parabola that has axis x = -1 and passes [3] through the points (4,5)…

A: Directrix is a line which together with a point called the focus defines the set of points that form…

Q: Determine whether this is a parabola: y = 5a + 80x + 321 . O Parabola Not a parabola If it is a…

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Q: Find an equation of the parabola drawn below: 2 Xx Select one: O a. (x + 2)2 = 2 (y + 2) O b.…

A: We have to find the equation of parabola.

Q: Determine the focus of the parabola (x - 2)² = 4(y - 3). %3D O (-1,-3) O (2,4) O (-2,-2) O (2,3)

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Q: State whether the equation x² + ()² + 6z² = 1 defines O a hyperboloid of two sheets. O a paraboloid…

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Q: Find the center and radius of a circle defined by the equation 2x + 2y? + 10x – 6y + 55 = 0. Sketch…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: = 8. Find the equations of both the tangent lines to the hyperbola x² - 4y² 9 that pass through the…

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Q: y? = t2 – 2t and x = t + 2 is I. Ellipse II. Circle III. Parabola IV. Hyperbola

A: topic - conics

Q: 1. Write the equation of a circle with a center at (-3, -4) and a radius of 7.

A: Given: Center of the circle=-3, -4Radius of the circle=7 To Find: The equation of the given circle

Q: What is the equation of a parabola that intersects the x-axis at points (-1, 0) and (3, 0)?   A. y…

A: Given that: A parabola intersects x-axis at (-1, 0) and (3, 0)

Q: Find the equation of the osculating circle of the parabola y= 1 x' at the point where x = 1. Then 4.…

A: The given data is: The equation of a parabola is: y=12x2 To find the equation of the osculating…

Q: #62. Civil engineers often design road surfaces with parabolic cross sections to provide water…

A: Given: Width of the road (w) =32 feet radius of the road (r)=322=16 feet rise at center of road 0.4…

Q: Graph the transformed parabola using the table of values method (i.e. with the mapping rule) Show…

A: Graph of this is given below

Q: Write an equation for the parabola

A: Find the equation of parabola from the given data .

Q: What is the standard form of equation of a parabola with vertex at the origin and directrix x = 3? A…

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Q: State whether the equation z - ()² = (+)² defines a hyperboloid of two sheets. an ellipsoid. a…

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Q: Find the equations of the osculating circles of the parabola y = 3(x – 2)2 at the points (2,0)

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Q: variable circle through the origin and touching the hyperbola xy = c

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Q: Consider the diagram below in a two dimensional Cartesian x-y plane. The parabola is given by the…

A: we will use symmetry of given figure about y-axis and condition of quadratic equation to find…

Q: Determine whether the statement is true or false. If the statement is false, make the necessary…

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Q: Write an equation of the parabola with its vertex at (x, y) - (3, 9) and focus at (x, y) (3,-2).

A: The parabola has vertex at (h,k)= (3, 9) and focus at (h,k+a)= (3, -2) Hence axis of symmetry is x=3…

Q: Write the equation of the parabola with focus at (3,5) and directrix y = 3.

A: First I have written a formula of parabola with given focus and directrix, just use the formula for…

Q: The sketch shows a circle, a parabola, which is the graph of f, and a straight line, which is the…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…